Accuracy of relativistic predictions of molecular parity-violating energies
In plain words
Calculations of the left-right energy difference must include relativity, electron correlation and molecular vibrations, and different methods can give answers differing by large factors. A trusted value with an error bar is needed before an experiment can test the weak force.
Precise statement
$\Delta E_{\mathrm{PV}}$ from the nuclear-spin-independent electron-nucleus weak interaction H_PV = (G_F / (2 sqrt 2)) sum_A Q_W(A) sum_i gamma_5(i) rho_A(r_i), computed with four-component Dirac-Coulomb or two-component Hamiltonians at DFT and coupled-cluster levels, including vibrational averaging and large-amplitude torsional motion. Question: for a chosen experimental candidate (e.g. CHFClBr, a Re or Os complex), what is $\Delta E_{\mathrm{PV}}$ and the vibrational-frequency difference with a total uncertainty below about 20 percent. An answer is converged values with error bars from at least two independent correlated relativistic methods.
What would settle it
Systematic four-component coupled-cluster calculations with vibrational averaging that agree with an independent method within the stated error for a molecule under experimental study.
Status in the literature
Unverified note
A 2025 study (Sunaga et al., J. Chem. Phys.) found strong parity-violation effects from large-amplitude motions, showing that vibrational treatment can change predictions substantially.